A Dynamic Regional Model of Irrigated Perennial Crop Production

Perennial crop production is inherently dynamic due to several salient physical characteristics including an establishment period of several years, long lives in commercial production, and pathdependence of yields on input use and other exogenous factors such as weather. While perennial crop production is properly regarded as a dynamic investment under uncertainty, the literature on regional agricultural production is typically static, deterministic, and rarely are the dynamic biophysical elements of perennial crops represented. This paper seeks to address some of the shortcomings of the literature by developing a dynamic regional model of irrigated agriculture with representative perennial and annual crops. The model explicitly accounts for the age composition of perennial stocks including crop establishment period and age-dependent yields and input use. The model is applied to wine grape production in the Riverland region of the Murray-Darling Basin (MDB) in Australia using a representative agricultural household to analyze joint consumption and investment decisions. Borrowing is allowed but the assumption of perfect capital markets is relaxed; the household faces an interest rate schedule that is increasing in the amount of debt held. We explore the dynamic properties of the model including the existence and uniqueness of a steady state and the conditions required for convergence to the steady state. Because the state-space required for an age-explicit regional model is too large for conventional dynamic programming methods, a running horizon algorithm is used to approximate an infinite horizon dynamic programming solution. The effects of the age structure of initial perennial plantings are investigated. Starting with an initial age distribution of grape stocks different from the steady state levels leads to dampened oscillations in area planted by vintage with eventual convergence to a steady state with an equal age distribution. The impact of water entitlement reductions for several possible scenarios under the proposed MDB Plan are estimated under both deterministic and stochastic frameworks, the latter of which is based on Monte Carlo simulations that draw on the distribution of historical water diversions in the region. Also, the long-run water demand for perennial crops is identified by systematically running simulations over varying water allocation levels and capturing the farmer’s marginal willingness to pay for water.